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0

$begingroup$

I want to prove that $T(G)=T(G)*T(G)$ where G is an infinite compact abelian Hausforff Topological group. I'm trying to start this but really im confused with the convolution. Say $f,g in T(G)$ I need to show that $f*g in T(G)$, so this is what im getting;

$f*g(x) = int_G f(sx)g(s^-1)ds = int_Gf(s)f(x)g(s^-1)ds$ but I'm not really sure where to go from there... this whole idea of convolution kind of confuses me and where can you go from $g(s^-1)$ can we say that this is $overlineg(s)$?

I'm also not sure how to approach the other direction... that as trig polynomial can be written as a convolution of two other trig polynomials.

analysis harmonic-analysis characters

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asked Mar 12 at 19:47

SashaSasha

708

$endgroup$

add a comment | 

0

$begingroup$

I want to prove that $T(G)=T(G)*T(G)$ where G is an infinite compact abelian Hausforff Topological group. I'm trying to start this but really im confused with the convolution. Say $f,g in T(G)$ I need to show that $f*g in T(G)$, so this is what im getting;

$f*g(x) = int_G f(sx)g(s^-1)ds = int_Gf(s)f(x)g(s^-1)ds$ but I'm not really sure where to go from there... this whole idea of convolution kind of confuses me and where can you go from $g(s^-1)$ can we say that this is $overlineg(s)$?

I'm also not sure how to approach the other direction... that as trig polynomial can be written as a convolution of two other trig polynomials.

analysis harmonic-analysis characters

share|cite|improve this question

asked Mar 12 at 19:47

SashaSasha

708

$endgroup$

add a comment | 

$begingroup$

I want to prove that $T(G)=T(G)*T(G)$ where G is an infinite compact abelian Hausforff Topological group. I'm trying to start this but really im confused with the convolution. Say $f,g in T(G)$ I need to show that $f*g in T(G)$, so this is what im getting;

$f*g(x) = int_G f(sx)g(s^-1)ds = int_Gf(s)f(x)g(s^-1)ds$ but I'm not really sure where to go from there... this whole idea of convolution kind of confuses me and where can you go from $g(s^-1)$ can we say that this is $overlineg(s)$?

I'm also not sure how to approach the other direction... that as trig polynomial can be written as a convolution of two other trig polynomials.

analysis harmonic-analysis characters

share|cite|improve this question

asked Mar 12 at 19:47

SashaSasha

708

$endgroup$

share|cite|improve this question

asked Mar 12 at 19:47

SashaSasha

708

share|cite|improve this question

asked Mar 12 at 19:47

SashaSasha

708

asked Mar 12 at 19:47

SashaSasha

708

asked Mar 12 at 19:47

SashaSasha

708